MCQ
Let $x=(\sqrt{50}+7)^{1 / 3}-(\sqrt{50}-7)^{1 / 3}$. Then,
- ✓$x=2$
- B$x=3$
- C$x$ is a rational number, but not an integer
- D$x$ is an irrational number
Given,
$x=(\sqrt{50}+7)^{1 / 3}-(\sqrt{50}-7)^{1 / 3}$
On cubing both sides, we get
$x^3=(\sqrt{50}+7)-(\sqrt{50}-7)-3$
$(\sqrt{50}+7)^{1 / 3}(\sqrt{50}-7)^{1 / 3}$
${\left[(\sqrt{50}+7)^{1 / 3}-(\sqrt{50}-7)^{1 / 3}\right] }$
$\Rightarrow \quad x^3=14-3(50-49)^{1 / 3}(x)$
$\Rightarrow \quad x^3=14-3 x$
$\Rightarrow \quad x^3+3 x-14=0$
$\Rightarrow(x-2)\left(x^2+2 x+7\right)=0$
$\Rightarrow \quad x=2$
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